Her brother, Jim Shapiro (Nina takes their mother’s surname), ponders this for a moment. ”After we’d played, like, eight shows, we were up in Milwaukee and [an A&R exec] said, ‘We want Veruca Salt to turn our label around the way — ”’ A venomous glare from his sister stops him dead. ”No?”

Veruca Salt have reason to fear flattery. The Chicago quartet — which also includes singer-guitarist Louise Post, 27, and bassist Steve Lack, 24 — rocketed from novice to Next Big Thing in less than a year. Miners of chart-ready noise-pop nuggets, they ignited a major-label bidding war over the summer that participants rank as the fiercest in memory. Last month, the group signed to alterna-heavyweight DGC Records (Nirvana, Beck, Counting Crows) for what a source involved in the negotiations calls ”the best new-artist deal ever” — a five-album contract that boasts an estimated $500,000 advance, with incentive formulas that escalate to a $2.5 million advance for the fifth record.

But Veruca Salt’s profile — encompassing every contemporary signpost of ”hot” — is both its blessing and its curse: The brightest blip on modern-rock’s radar screen threatens to become more emblem than act.

Even their atypically highbrow roots evince Gen X hallmarks. Drummer Shapiro, 29, and singer-guitarist Gordon, 26, children of a Chicago lawyer, accumulated their musical experience on a relatively privileged plane — he at Yale as bassist in a band named U Thant, she on a year abroad from Tufts in Paris (learning chords from her brother over the phone). Both eventually returned home after college, slackened by unrelated bouts of ennui: ”I was depressed and paralyzed — virtually shiftless,” says Shapiro. Echoes Gordon, ”I didn’t have a plan; I had this open-ended life.”

Focus solidified in the form of Post — a St. Louis native who majored in English at Barnard. Introduced in early 1992, she and Gordon started collaborating on songs; a Chicago Reader ad tossed up Lack — a funeral director’s son whose series of bands, he says, ”never really got out of the coffin room” in which they practiced.